Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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(b) Let a > 0, and let X = C(|-a,a];R) be the space of continuous real-valued functions defined on [-a, a] equipped with the supremum metric d, defined by d»(f,8) = sup \f (x) – 8(x)|, x€l-a,a) for all f,8 € X. Using the Contraction Mapping Theorem, prove that the integral equation 1 f6) = 1+ 2 권 f0) dh, 1+(x-t) - x€ (-a,a) has a unique solution f in X. Justify any assertions that you make.
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Transcribed Image Text:(b) Let a > 0, and let X = C(|-a,a];R) be the space of continuous real-valued functions defined on [-a, a] equipped with the supremum metric d, defined by d»(f,8) = sup \f (x) – 8(x)|, x€l-a,a) for all f,8 € X. Using the Contraction Mapping Theorem, prove that the integral equation 1 f6) = 1+ 2 권 f0) dh, 1+(x-t) - x€ (-a,a) has a unique solution f in X. Justify any assertions that you make.
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